Geometric Optics with Mirrors: How Reflection Creates Images

Reflection

The process in which light hits a boundary and bounces back into the original medium; in geometric optics it describes how rays change direction at a surface.

Ray (geometric optics)

An ideal straight-line representation of light’s path used to predict reflection and image formation.

Normal

A line drawn perpendicular to a surface at the point where a ray strikes; all reflection angles are measured from this line.

Angle of incidence (θi)

The angle between the incoming ray and the normal to the surface.

Angle of reflection (θr)

The angle between the reflected ray and the normal to the surface.

Law of reflection

Rule stating that the angle of incidence equals the angle of reflection: θi = θr (angles measured from the normal).

Specular reflection

Reflection from a smooth surface where parallel incoming rays reflect as parallel rays, preserving image information (mirror-like).

Diffuse reflection

Reflection from a rough surface where each tiny patch obeys θi = θr, but varying local normals send reflected rays in many directions (no sharp image).

Plane mirror

A flat reflective surface that forms a virtual, upright, same-size image appearing the same distance behind the mirror as the object is in front.

Path reversal

Principle that a light path that works from A to B by the law of reflection will also work from B to A along the same path.

Image (geometric optics)

A location where rays actually converge (real image) or appear to originate from when traced backward (virtual image).

Real image

An image formed where light rays physically converge; it can be projected onto a screen (typically di > 0 for mirrors under the common convention).

Virtual image

An image location from which rays only appear to originate when traced backward; it cannot be projected onto a screen (typically di < 0 for mirrors).

Lateral inversion

Left-right reversal produced by a plane mirror image; not the same as upside-down inversion.

Spherical mirror

A mirror shaped as a section of a sphere; includes concave and convex mirrors and is analyzed using focal length and the mirror equation.

Concave mirror (converging mirror)

A spherical mirror with reflective surface on the inside; can focus parallel rays to a real focal point and can form real or virtual images depending on object position.

Convex mirror (diverging mirror)

A spherical mirror with reflective surface on the outside; spreads rays so they appear to come from a focal point behind the mirror and (for real objects) forms virtual, upright, reduced images.

Principal axis

The central line through a spherical mirror’s vertex (midpoint) and the center of curvature; used as the reference for ray diagrams.

Center of curvature

The center of the sphere of which the spherical mirror is a part.

Radius of curvature (R)

Distance from the mirror’s vertex to the center of curvature.

Focal point (focus)

Point where rays parallel to the principal axis reflect to (concave) or appear to originate from (convex).

Focal length (f)

Distance from the mirror’s vertex to the focal point; for spherical mirrors (paraxial approximation), f = R/2.

Mirror equation

Relationship for spherical mirrors: 1/f = 1/do + 1/di, connecting focal length, object distance, and image distance (including signs).

Magnification (m)

Ratio describing image size and orientation: m = hi/ho = −di/do; |m|>1 magnified, |m|

Mirror sign convention (common “real is positive”)

A consistent sign system: do > 0 for a real object in front of the mirror; di > 0 for real images in front and di < 0 for virtual images behind; f > 0 for concave mirrors and f < 0 for convex mirrors.